Yes. You can install an application to use the OpenStreetMap data in off-line mode. The best application for Android to date that I know that works worldwide is OsmAnd, which is a free and open source application, but it comes also with a paid version to support the author. For the United Kingdom, however, there's a good application called CycleStreets — but as far as I know they don't provide non-UK data dumps for you to use in Denmark.

Try choosing different candidates from the combo box near the next map (not OSM, presumably, but the official cadastre rather, I think). It distorts the map in fish eye style and display nice animation of a histogram being sorted :)